Numerical performance of finite-difference modal methods for the electromagnetic analysis of one-dimensional lamellar gratings

The numerical performance of a finite-difference modal method for the analy sis of one-dimensional lamellar gratings in a classical mounting is studied . The method is simple and relies on first-order finite difference in the g rating to solve the Maxwell differential equations. The finite-difference s cheme incorporates three features that accelerate the convergence performan ce of the method: (1) The discrete permittivity is interpolated at the lame llar boundaries, (2) mesh points are located on the permittivity discontinu ities, and (3) a nonuniform sampling with increased resolution is performed near the discontinuities. Although the performance achieved with the prese nt method remains inferior to that achieved with up-to-date grating theorie s such as rigorous coupled-wave analysis with adaptive spatial resolution, it is found that the present method offers rather good performance for meta llic gratings operating in the visible and near-infrared regions of the spe ctrum, especially for TM polarization. (C) 2000 Optical Society of America [S0740-3232(00)00606-2].